back to *algebra*
# Polynomials

**Monomial**- Monomial is an algebra expression in which there is only the product of number and variables

**Examples**- The product of number and positive exponent of variables. Only a number or a variable is also a monomial.

**Coefficient of a Monomial**- The number in a monomial is called the coefficient of the monomial.

**Examples**

**Degree of a Monomial**- The sum of exponent of all variables in a monomial is called the degree of the monomial.

**Examples**- For monomial 2x
^{3}y^{2}, the exponent of variable x is 3, and the exponent of variable y is 2, the sum of the exponents x and y is 5, therefor, monomial 2x^{3}y^{2}has the degree of five.

**Polynomial**- The sum of one or more monomial is called polynomial. Monomial is a special case of polynomial.

**Example**

**Terms in a Polynomial**- Each monomial is called a term of the polynomial.

**Example**- polynomial 9x
^{2}- 6x + 1 has three term, first term is 9x^{2}, second term is -6x, the third term is 1.

**Constant Term in a Polynomial**- A term which has no any variable is called a constant term.

**Example**- In polynomial 2x + 3, the constant term is 3.

**Degree of a Polynomial**- The degree of a polynomial is the largest degree of any term.

**Example**- polynomial 5y
^{2}+ 8y - 6 has three terms, the first term is 5y^{2}, the variable y has an exponent of 2, so the first term has degree of 2, second term is 8y, the variable y has exponent of 1, so the second term has degree of 1, the third term is a constant, so the degree of the third term is zero. Therefore, the degree of this polynomial is 2, it is two degree three terms polynomial.

**Descending Power of One Variable in a Polynomial**- Order a polynomial as descending power of one variable with the term of largest degree of that variable first.

**Example**

**Ascending Power of One Variable in a Polynomial**- Order a polynomial as ascending power of one variable with the term of the lowest degree of that variable first.

**Example**

**Similar Terms or Like Term**- If two or more terms in a polynomial have the same veriable name and the same variable name has same exponent, then these terms are similar (like) terms. Constant terms are similar (like) terms.

**Example**- 2x
^{2}and 6x^{2}are similar (like) terms, +3y and -2y are similar (like) terms, +6 and +5 are similar (like) terms.

**Combination of Similar Terms**- In a polynomials, combine similar terms into only one term is called combination of similar term.

**Example**- when add similar (like) terms, we only add their coefficient and keep variable and exponent the same, 3y + (-2y) = 3y - 2y = y.

**Rules of Combining Similar Terms**- Add coefficient of all similar terms in a polynomial, the result is the new coefficient of the term in which variables name and the exponent of variable name keep the same.

**Example**- If two similar terms have opposite coefficient, the combination of the two terms is zero. If there is no similar terms in a polynomial, you need to keep the term for this polynomial.

**Rules of Remove Parenthesis (Addition of Polynomial)**- If there is a
*"+" sign in front of the parenthesis*, each term inside the parenthesis keep the same when remove the parenthesis and the "+" sign in front of the parenthesis.

**Example**

**Rules of Remove Parenthesis (Subtration of Polynomial)**- If there is a
*"-" sign in front of the parenthesis*, every term inside the parenthesis must has its sign changed to its opposite sign when remove the parenthesis and the "-" sign in front of parenthesis.

**Example**

**Rules of Adding Parenthesis ("+" in Front of Parenthesis)**- If there is a "+" sign in front of the parenthesis, each term inside the parenthesis keep the same sign.

**Example**

**Rules of Adding Parenthesis ("-" in Front of Parenthesis)**- If there is a "-" sign in front of the parenthesis, every term inside the parenthesis must has its sign changed to its opposite sign.

**Example**